Tag: shortcut method to find variance and standard deviation

The mean of t distribution is always equal to 0 and also the variance is always greater than 1 and it is symmetrical like normal distribution.

Standard error can be calculated by applying two formulas mentioned in option A and option B that shows how a sample mean deviates from the mean of whole population.

Chi square distribution is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.

In the curve, with the large sample size, there are more samples with a mean around the middle and fewer with sample means at the extreme, the curve becomes more symmetrical. Larger samples tend to have lower standard errors

Both (a) and (b) statements regarding students t-distribution is correct i.e. its value varies from +infinity to-infinity and the variance of t distribution and the variance of normal distribution become closer and closer as the sample size increases and also the variance of t distribution is always greater than 1.

If the sample size of the population is small, then the curve would be skewed on one side and also as the sample size increases the sampling distribution of the mean gets narrower.

If the standard deviation is small, it signifies that data are closely distributed around the mean value instead of widely spread and here, we define a new variable as Students T-variable.